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Question

In the expansion of (31/7+51/2)14, which of the following is true?

A
number of rational terms is 3
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B
number of irrational terms is 12
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C
the sum of last two digits of rational terms is 34
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D
seventh term is the middle term
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Solution

The correct option is C the sum of last two digits of rational terms is 34
In the expansion of (31/7+51/2)14,
Tr+1= 14Cr(31/7)14r(51/2)r, r=0,1,2,,14
= 14Cr 3(2r7)5r/2

There are only two rational terms, when r=0,14
So, rational terms are, T1=32 and T15=57

Total number of terms =14+1=15

Number of irrational terms =152=13

Sum of last two digits of rational terms =32+57=9+_ _ _ 25=_ _ _ 34

Since, total number of terms is 15 i.e. odd,
Middle term =15+12=8

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